Zigzag strip bundles and crystals

초록

We introduce new combinatorial models, called zigzag strip bundles, over quantum affine algebras U-q(B-n((1))), U-q(D-n((1))) and U-q(D-n+1((2))), and show that the sets of all zigzag strip bundles for U-q(B-n((1))), U-q(D-n((1))) and U-q(D-n+1((2))) realize the crystal bases B(infinity) of U-q(-)(B-n((1))), U-q(-)(D-n((1))) and U-q(-)(D-n+1((2))), respectively. Further, we discuss the connection between zigzag strip bundle realization, Nakajima monomial realization, and polyhedral realization of the crystal B(infinity).

키워드